2.3.194 Problems 19301 to 19400

Table 2.961: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
19301	8026	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=\ln \left (x \right )^{2}-\ln \left (x^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	3.178
19302	15600	\begin{align*} y^{\prime }&=\frac {2 y}{x}+{\mathrm e}^{x} \\ y \left (1\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✓	3.178
19303	17645	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +4 y&=0 \\ y \left (1\right ) &= -1 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.178
19304	3963	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=1-3 \operatorname {Heaviside}\left (-2+t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	3.179
19305	12695	\begin{align*} y^{\prime \prime }&=-\frac {\cos \left (x \right ) y^{\prime }}{\sin \left (x \right )}-\frac {\left (-17 \sin \left (x \right )^{2}-1\right ) y}{4 \sin \left (x \right )^{2}} \\ \end{align*}	✓	✓	✓	✗	3.179
19306	711	\begin{align*} y+3 y^{\prime } x&=12 x \\ \end{align*}	✓	✓	✓	✓	3.180
19307	10019	\begin{align*} p^{\prime }&=a p-b p^{2} \\ p \left (\operatorname {t0} \right ) &= \operatorname {p0} \\ \end{align*}	✓	✓	✓	✓	3.180
19308	18495	\begin{align*} y^{\prime }&=\frac {-{\mathrm e}^{x}+3 x^{2}}{2 y-11} \\ y \left (0\right ) &= 11 \\ \end{align*}	✓	✓	✓	✓	3.181
19309	27439	\begin{align*} 3 {y^{\prime }}^{3}-y^{\prime } x +1&=0 \\ \end{align*}	✓	✓	✓	✓	3.181
19310	1151	\begin{align*} y^{\prime }&=2 y^{2}+x y^{2} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.182
19311	8675	\begin{align*} 2 x \sqrt {1-y^{2}}+y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.182
19312	14481	\begin{align*} y^{\prime }+\frac {3 y}{x}&=6 x^{2} \\ \end{align*}	✓	✓	✓	✓	3.182
19313	4333	\begin{align*} x^{2}-\sin \left (y\right )^{2}+x \sin \left (2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.184
19314	12448	\begin{align*} x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y-5 x&=0 \\ \end{align*}	✓	✓	✓	✓	3.184
19315	12389	\begin{align*} y^{\prime \prime } x -\left (2 a \,x^{2}+1\right ) y^{\prime }+b \,x^{3} y&=0 \\ \end{align*}	✓	✓	✓	✗	3.185
19316	12934	\begin{align*} y y^{\prime \prime }-{y^{\prime }}^{2}+\left (g \left (x \right )+f \left (x \right ) y^{2}\right ) y^{\prime }-y \left (g^{\prime }\left (x \right )-f^{\prime }\left (x \right ) y^{2}\right )&=0 \\ \end{align*}	✗	✗	✓	✗	3.187
19317	20444	\begin{align*} y&=a y^{\prime }+b {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	3.187
19318	1617	\begin{align*} y^{\prime }&=x \left (-1+y^{2}\right )^{{2}/{3}} \\ \end{align*}	✓	✓	✓	✓	3.189
19319	27003	\begin{align*} x^{2} y^{\prime \prime }-5 y^{\prime } x +58 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.189
19320	11572	\begin{align*} \left (y^{2}+4 \sin \left (x \right )\right ) y^{\prime }-\cos \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	3.190
19321	2990	\begin{align*} y^{\prime }-y x&=\frac {x}{y} \\ \end{align*}	✓	✓	✓	✓	3.191
19322	12296	\begin{align*} y^{\prime \prime }+\left (a \,x^{2 c}+b \,x^{c -1}\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	3.191
19323	20655	\begin{align*} x^{4} y^{\prime \prime }+2 x^{3} y^{\prime }+n^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	3.191
19324	23194	\begin{align*} y-y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	3.191
19325	13376	\begin{align*} \left (a \sin \left (\lambda x \right )+b \right ) y^{\prime }&=y^{2}+c \sin \left (\mu x \right ) y-d^{2}+c d \sin \left (\mu x \right ) \\ \end{align*}	✓	✓	✓	✗	3.192
19326	3971	\begin{align*} -y+y^{\prime }&=\left \{\begin {array}{cc} 2 & 0\le t <1 \\ -1 & 1\le t \end {array}\right . \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	3.193
19327	3669	\begin{align*} y^{\prime }+\frac {2 x y}{x^{2}+1}&=x y^{2} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.194
19328	4706	\begin{align*} y^{\prime }&=\sqrt {{| y|}} \\ \end{align*}	✓	✓	✓	✓	3.194
19329	24976	\begin{align*} \frac {\left (u^{2}+1\right ) y^{\prime }}{y}&=u \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✗	3.194
19330	14890	\begin{align*} y^{\prime }&=y^{2} {\mathrm e}^{-t^{2}} \\ \end{align*}	✓	✓	✓	✓	3.195
19331	8428	\begin{align*} -y+y^{\prime } x&=x^{2} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	3.196
19332	1849	\begin{align*} x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (2 x +1\right ) y^{\prime }-\left (6 x +4\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	3.198
19333	11826	\begin{align*} 2 y {y^{\prime }}^{3}-y {y^{\prime }}^{2}+2 y^{\prime } x -x&=0 \\ \end{align*}	✓	✓	✓	✓	3.198
19334	1596	\begin{align*} y^{\prime }&=2 y-y^{2} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.200
19335	17318	\begin{align*} 3 y+y^{\prime }&=-10 \sin \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	3.200
19336	21043	\begin{align*} x^{\prime }&=x^{3}-x \\ x \left (0\right ) &= a \\ \end{align*}	✓	✓	✓	✓	3.200
19337	22036	\begin{align*} y^{\prime } x -y+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	3.200
19338	1520	\begin{align*} y^{\prime } x +y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	3.201
19339	16478	\begin{align*} x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.201
19340	22445	\begin{align*} 2 x +2 x y^{2}+\left (x^{2} y+2 y+3 y^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.202
19341	3304	\begin{align*} y {y^{\prime }}^{2}+2 y^{\prime }+1&=0 \\ \end{align*}	✓	✓	✓	✗	3.203
19342	17362	\begin{align*} t^{2} y^{\prime \prime }+y^{\prime } t -y&=0 \\ \end{align*}	✓	✓	✓	✓	3.203
19343	5189	\begin{align*} \left (-x^{2}+1\right ) y y^{\prime }+2 x^{2}+x y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	3.204
19344	14258	\begin{align*} \cos \left (\theta \right ) v^{\prime }+v&=3 \\ \end{align*}	✓	✓	✓	✓	3.204
19345	8223	\begin{align*} y^{\prime } x&=2 y \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	3.205
19346	5239	\begin{align*} 3 y^{2} y^{\prime }&=1+x +a y^{3} \\ \end{align*}	✓	✓	✓	✓	3.206
19347	9257	\begin{align*} y^{\prime \prime }+9 y&=2 \sin \left (3 x \right )+4 \sin \left (x \right )-26 \,{\mathrm e}^{-2 x}+27 x^{3} \\ \end{align*}	✓	✓	✓	✓	3.207
19348	11898	\begin{align*} y^{\prime }&=\frac {y}{x \left (-1+F \left (y x \right ) y\right )} \\ \end{align*}	✓	✓	✓	✗	3.207
19349	26052	\begin{align*} {y^{\prime }}^{3}&=a \,x^{4} \\ \end{align*}	✓	✓	✓	✓	3.207
19350	17007	\begin{align*} y^{\prime } x +y&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	3.208
19351	17388	\begin{align*} y^{\prime \prime }+8 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.210
19352	1121	\begin{align*} \left (1+t \right ) y+y^{\prime } t&=2 t \,{\mathrm e}^{-t} \\ y \left (1\right ) &= a \\ \end{align*}	✓	✓	✓	✓	3.211
19353	3519	\begin{align*} y^{\prime }&=\frac {2 x \left (-1+y\right )}{x^{2}+3} \\ \end{align*}	✓	✓	✓	✓	3.211
19354	5970	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✓	3.211
19355	21083	\begin{align*} y y^{\prime } x +1+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	3.211
19356	21321	\begin{align*} x^{\prime \prime }+\lambda x-x^{3}&=0 \\ x \left (0\right ) &= 0 \\ x \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✗	✗	3.212
19357	4725	\begin{align*} y^{\prime }+\sin \left (2 x \right ) \csc \left (2 y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	3.213
19358	773	\begin{align*} y x +y^{2}-x^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.214
19359	15537	\begin{align*} y^{\prime }&=\frac {y}{x} \\ \end{align*}	✓	✓	✓	✓	3.214
19360	22548	\begin{align*} x^{2} y+\left (x^{3}+1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.214
19361	27263	\begin{align*} y^{\prime }+\tan \left (x \right ) y&=\sec \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	3.214
19362	9769	\begin{align*} 2 a y^{\prime \prime }+{y^{\prime }}^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	3.215
19363	11306	\begin{align*} y^{\prime }+2 y x -x \,{\mathrm e}^{-x^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	3.215
19364	24295	\begin{align*} y&=\left (2 x +1\right ) \left (1-y^{\prime }\right ) \\ \end{align*}	✓	✓	✓	✓	3.216
19365	17886	\begin{align*} 2 x \sqrt {1-y^{2}}&=\left (x^{2}+1\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	3.217
19366	3473	\begin{align*} y^{\prime }-\frac {y}{x}&=1 \\ y \left (1\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	3.218
19367	3697	\begin{align*} y^{\prime \prime }-36 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.218
19368	19362	\begin{align*} 2 y y^{\prime \prime }&=1+{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	3.219
19369	7253	\begin{align*} y^{\prime }&=\cos \left (x +y\right ) \\ \end{align*}	✓	✓	✓	✓	3.220
19370	7357	\begin{align*} -y+y^{\prime } x&=x^{2} \\ y \left (2\right ) &= 6 \\ \end{align*}	✓	✓	✓	✓	3.220
19371	8777	\begin{align*} y^{\prime }&=x^{2} \left (1+y^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	3.220
19372	24995	\begin{align*} y^{\prime }+a y&=t^{n} {\mathrm e}^{-a t} \\ \end{align*}	✓	✓	✓	✓	3.220
19373	1802	\begin{align*} x^{2} \left (y^{\prime }+y^{2}\right )+y x +x^{2}-\frac {1}{4}&=0 \\ \end{align*}	✓	✓	✓	✓	3.221
19374	19979	\begin{align*} x {y^{\prime }}^{2}-2 y y^{\prime }+a x&=0 \\ \end{align*}	✓	✓	✗	✓	3.221
19375	3520	\begin{align*} y-y^{\prime } x&=3-2 x^{2} y^{\prime } \\ \end{align*}	✓	✓	✓	✓	3.222
19376	5588	\begin{align*} \left (x +y\right )^{2} {y^{\prime }}^{2}-\left (x^{2}-y x -2 y^{2}\right ) y^{\prime }-y \left (x -y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	3.223
19377	9133	\begin{align*} 1+y+\left (1-x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.223
19378	23880	\begin{align*} x^{2} y-2 x +\left (\frac {x^{3}}{3}+y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.223
19379	4508	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +y&=\ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	3.224
19380	7225	\begin{align*} \left (1+y\right ) y^{\prime }&=y \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.224
19381	8389	\begin{align*} y^{\prime }&=y-y^{3} \\ y \left (0\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✗	✓	3.224
19382	8397	\begin{align*} y^{\prime }&=\frac {\sin \left (\sqrt {x}\right )}{\sqrt {y}} \\ \end{align*}	✓	✓	✓	✓	3.224
19383	16560	\begin{align*} x^{2} y^{\prime \prime }-5 y^{\prime } x +29 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.224
19384	2986	\begin{align*} y^{\prime }-y x&=\sqrt {y}\, x \,{\mathrm e}^{x^{2}} \\ \end{align*}	✓	✓	✓	✓	3.225
19385	12453	\begin{align*} x^{2} y^{\prime \prime }+a x y^{\prime }+b y&=0 \\ \end{align*}	✓	✓	✓	✓	3.225
19386	27022	\begin{align*} y^{\prime \prime }+4 y&=\left \{\begin {array}{cc} 0 & 0\le t <4 \\ 3 & 4\le t \end {array}\right . \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	3.225
19387	19789	\begin{align*} y^{\prime }+\frac {y}{x}&=-x^{2}+1 \\ \end{align*}	✓	✓	✓	✓	3.227
19388	22998	\begin{align*} v^{\prime }&=60 t -4 v \\ v \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.227
19389	26189	\begin{align*} y^{\prime }&=\left (-1+y\right ) x \\ \end{align*}	✓	✓	✓	✓	3.227
19390	18550	\begin{align*} y+\ln \left (t \right ) y^{\prime }&=\cot \left (t \right ) \\ y \left (2\right ) &= 3 \\ \end{align*}	✓	✓	✓	✗	3.228
19391	768	\begin{align*} {\mathrm e}^{x} \sin \left (y\right )+\tan \left (y\right )+\left ({\mathrm e}^{x} \cos \left (y\right )+x \sec \left (y\right )^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.229
19392	15847	\begin{align*} y^{\prime }&=2 y^{3}+t^{2} \\ y \left (0\right ) &= -{\frac {1}{2}} \\ \end{align*}	✗	✗	✗	✗	3.229
19393	22177	\begin{align*} \left (x +1\right ) y^{\prime \prime }+\frac {y^{\prime }}{x}+y x&=0 \\ \end{align*} Series expansion around \(x=-1\).	✓	✓	✓	✓	3.229
19394	3317	\begin{align*} y&=y^{\prime } x \left (1+y^{\prime }\right ) \\ \end{align*}	✓	✓	✓	✓	3.230
19395	21050	\begin{align*} x^{\prime }&=x^{2}-1 \\ x \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	3.230
19396	15799	\begin{align*} y^{\prime }&=-y^{2} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	3.231
19397	20824	\begin{align*} x^{2}+y-y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	3.233
19398	23106	\begin{align*} y^{\prime \prime }-\tan \left (x \right ) y^{\prime }-\frac {\tan \left (x \right ) y}{x}&=\frac {y^{3}}{x^{3}} \\ \end{align*}	✗	✗	✗	✗	3.233
19399	10375	\begin{align*} {y^{\prime \prime }}^{2}+y^{\prime }&=1 \\ \end{align*}	✓	✓	✓	✓	3.236
19400	19631	\begin{align*} y^{\prime \prime }+x^{2} y&=0 \\ y \left (0\right ) &= y_{0} \\ y^{\prime }\left (0\right ) &= \operatorname {yd}_{0} \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	3.236